Liouville theorem and classification of positive solutions for a fractional Choquard type equation

被引：28
作者：
Phuong Le [1 ,2 ]
机构：
[1] Ton Duc Thang Univ, Inst Computat Sci, Div Computat Math & Engn, Ho Chi Minh City, Vietnam
[2] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2019年 / 185卷
关键词：
Fractional Choquard equations; Liouville theorems; Classification of positive solutions; HARTREE-EQUATIONS; REGULARITY; UNIQUENESS; EXISTENCE; STATE;
D O I：
10.1016/j.na.2019.03.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let n >= 2, 0 < alpha < 2 and 0 < beta < n. We prove that the equation (- Delta)(alpha/2) u = (1/vertical bar x vertical bar(n-beta) * u(p)) u(p-1) in R-n has no positive solution if 1 <= p < n+beta/n-alpha. We also classify all positive solutions to the equation in the critical case p = n+beta/n-alpha. (C) 2019 Elsevier Ltd. All rights reserved.
引用
收藏
页码：123 / 141
页数：19
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